Some remarks on conformal invariant theories on four-lorentz manifolds

Contrary to the eleven-parameter group consisting of Poincaré-transformations and dilatations, the group of so-called special conformal transformations can act on the Minkowski space only as a local conformal Lie transformation group. We show that the universal covering space of the compactified Minkowski space , together with an appropriate metric (tilde g) on it, form a suitable Lorentz manifold that admits universal covering group of the “conformal group” of as a transitive Lie transformation group. This group respects the causality notion on usually defined on a Lorentz manifold. However, possesses only seven isometries in contrast to the well-known ten isometries on the Minkowski space , which correspond to conservation of energy-momentum and angular-momentum.